An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms

In this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi...

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Main Author: Md Aquib
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/3/213
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author Md Aquib
author_facet Md Aquib
author_sort Md Aquib
collection DOAJ
description In this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-Casorati curvatures of warped product pointwise semi-slant (WPPSS) submanifolds within complex space forms. We further identify the precise conditions under which these inequalities attain equality, providing valuable insights into their geometric and structural significance. Additionally, we also present results involving harmonic and Hessian functions, revealing a broader connection between curvature properties and analytic functions.
format Article
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spelling doaj-art-618662ee674948469d5ab79fdcfe01842025-08-20T02:42:45ZengMDPI AGAxioms2075-16802025-03-0114321310.3390/axioms14030213An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space FormsMd Aquib0Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi ArabiaIn this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-Casorati curvatures of warped product pointwise semi-slant (WPPSS) submanifolds within complex space forms. We further identify the precise conditions under which these inequalities attain equality, providing valuable insights into their geometric and structural significance. Additionally, we also present results involving harmonic and Hessian functions, revealing a broader connection between curvature properties and analytic functions.https://www.mdpi.com/2075-1680/14/3/213Casorati curvaturesemi-slant submanifoldwarped product submanifoldcomplex space formharmonic functionHessian function
spellingShingle Md Aquib
An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms
Axioms
Casorati curvature
semi-slant submanifold
warped product submanifold
complex space form
harmonic function
Hessian function
title An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms
title_full An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms
title_fullStr An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms
title_full_unstemmed An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms
title_short An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms
title_sort optimal inequality for warped product pointwise semi slant submanifolds in complex space forms
topic Casorati curvature
semi-slant submanifold
warped product submanifold
complex space form
harmonic function
Hessian function
url https://www.mdpi.com/2075-1680/14/3/213
work_keys_str_mv AT mdaquib anoptimalinequalityforwarpedproductpointwisesemislantsubmanifoldsincomplexspaceforms
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